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arXiv · 2506.15296

Exact results on the Bethe Ansatz evaluation of the SCI

Antonio Amariti·Pietro Glorioso
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Abstract

We evaluate the superconformal index using the Bethe Ansatz (BA) approach for 4d $\mathcal{N}=1$ toric quiver gauge theories with a small amount of gauge groups. We restrict to $\mathrm{SU}(2)$ gauge factors and compare the results with the ones obtained by a direct evaluation of the index. The answer obtained from the BA approach using only discrete solutions for the BA equations does not always reproduce the direct evaluation result. A similar problem affects the case of $\mathrm{SU}(N)$ $\mathcal{N}=4$ SYM for $N \geq 3$, and it requires to introduce continuous solutions to the BA equations. However, we find that for $T^{1,1}$ and partially for the suspended pinch point the matching is exact in absence of the contributions from continuous solutions.

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Antonio Amariti, Pietro Glorioso. 2025-06-18. Exact results on the Bethe Ansatz evaluation of the SCI. https://arxiv.org/abs/2506.15296

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